The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is
A) .0241.
B) .0771.
C) .1126.
D) .9107.

Question

Quizplus · Accepted Answer

We are given that the random variable x follows a Poisson distribution, where the mean (λ) equals 5.3.

Then, we can use the formula for Poisson probability mass function:

P(x=k) = (e^(-λ) * λ^k) / k!

where k is the number of occurrences we're interested in.

Plugging in k=8 and λ=5.3, we get:

P(x=8) = (e^(-5.3) * 5.3^8) / 8!

P(x=8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to choice B.

The Random Variable X Is the Number of Occurrences of an Event